FINDING THE POINT OF DISCONTINUITY WORKSHEET

Find any points of discontinuity for each rational function.

Problem 1 :

y = (x + 3)/(x – 4) (x + 3)

Solution

Problem 2 :

y = (x - 2)/(x² – 4)

Solution

Problem 3 :

y = (x - 3) (x + 1)/(x – 2)

Solution

Problem 4 :

y = 3x(x + 2)/x(x + 2)

Solution

Problem 5 :

y = 2/(x + 1)

Solution

Problem 6 :

y = 4x/(x³ – 9x)

Solution

Find the points of discontinuity.  Classify each  point as a vertical asymptote or a hole.

Problem 1 :

y = x/(x² – 9)

Solution

Problem 2 :

y = (3x² – 1)/x³

Solution

Problem 3 :

y = (6x² + 3)/(x – 1)

Solution

Problem 4 :

y = (5x³ – 4)/(x² + 4x – 5)

Solution

Problem 5 :

y = 7x/(x³ + 1)

Solution

Problem 6 :

y = (12x⁴ + 10x – 3)/3x⁴

Solution

Problem 7 :

y = (12x + 24)/(x² + 2x)

Solution

Problem 8 :

y = (x² – 1)/(x² + 3x + 2)

Solution

Problem 9 :

y = (x² – 1)/(x² - 2x - 3)

Solution